Frequency Calculator
A Frequency Calculator is an essential tool for electronics engineers, physicists, and students that calculates frequency from various inputs like time period, wavelength, or angular frequency. Frequency, measured in Hertz (Hz), represents how often a repeating event occurs per second and is fundamental to wave physics, electronics, and signal processing.
Frequency calculations are critical for designing oscillators, filters, radio transmitters, audio equipment, and digital circuits. Understanding frequency relationships helps in troubleshooting circuits, analyzing signals, and designing systems that operate at specific frequencies for optimal performance.
Common applications of frequency calculations:
- Circuit Design: Determining resonant frequencies for LC circuits
- Signal Processing: Setting sampling rates and filter cutoffs
- Communications: Allocating frequencies for wireless transmission
- Audio Engineering: Tuning instruments and equalizing sound systems
Our frequency calculator handles four common calculation types with automatic unit conversion:
- Frequency from Period: Enter time period (T) → Get frequency (f = 1/T)
- Frequency from Wavelength: Enter wavelength (λ) and wave velocity (v) → Get frequency (f = v/λ)
- Frequency from Angular Frequency: Enter angular frequency (ω) → Get frequency (f = ω/2π)
- Period from Frequency: Enter frequency (f) → Get time period (T = 1/f)
Automatic features:
- Unit conversion: Automatically converts between Hz, kHz, MHz, GHz
- Pre-set values: Common wave velocities (light, sound in air/water)
- Real-time calculation: Updates as you type or change units
- Multiple outputs: Shows results in all relevant units
Different frequency ranges serve different purposes in technology and nature:
| Frequency Range | Name | Typical Applications | Example Period |
|---|---|---|---|
| 0.1 - 20 Hz | Extremely Low (ELF) | Geophysics, brain waves | 10 - 0.05 s |
| 20 - 20,000 Hz | Audio Frequency | Human hearing, music, voice | 50 - 0.05 ms |
| 20 kHz - 300 GHz | Radio Frequency | Radio, TV, WiFi, Bluetooth | 50 µs - 3.3 ps |
| 300 GHz - 30 THz | Terahertz | Security scanning, spectroscopy | 3.3 - 0.033 ps |
| 30 - 300 THz | Infrared | Remote controls, heat sensing | 33 - 3.3 fs |
| 430 - 790 THz | Visible Light | Vision, lasers, fiber optics | 2.3 - 1.3 fs |
Light wavelength to frequency: f(THz) ≈ 300 / λ(µm). Sound wavelength to frequency: f(Hz) ≈ 343 / λ(m). Time to frequency: f(kHz) = 1 / T(ms).
Below are answers to frequently asked questions about frequency calculations:
Frequency and wavelength have an inverse relationship because wave velocity is constant for a given medium:
- Basic equation: v = f × λ (velocity = frequency × wavelength)
- Constant velocity: For a given medium (air, water, vacuum), v is fixed
- Inverse relationship: If λ decreases, f must increase to maintain v = constant
- Example for light: Red light (700nm) ≈ 430THz, Blue light (450nm) ≈ 667THz
This relationship explains why higher frequency electromagnetic waves (like X-rays) have shorter wavelengths than lower frequency waves (like radio waves).
These three fundamental wave properties are mathematically related but conceptually different:
| Property | Definition | Unit | Relationship |
|---|---|---|---|
| Frequency (f) | Cycles per second | Hertz (Hz) | f = 1/T |
| Period (T) | Time per cycle | Seconds (s) | T = 1/f |
| Wavelength (λ) | Distance per cycle | Meters (m) | λ = v/f |
Use our calculator to convert between these properties easily.
Different circuit components determine frequency in various ways:
| Circuit Type | Frequency Formula | Example Calculation | Application |
|---|---|---|---|
| LC Oscillator | f = 1/(2π√LC) | L=1mH, C=1nF → f=159kHz | Radio tuning |
| RC Oscillator | f = 1/(2πRC) | R=10kΩ, C=1µF → f=15.9Hz | Low-frequency clock |
| Crystal Oscillator | Fixed by crystal | Common: 32.768kHz, 16MHz | Microcontroller clock |
| 555 Timer | f = 1.44/((R1+2R2)C) | R1=R2=10kΩ, C=1µF → f=48Hz | PWM generation |
Use our calculator for basic f=1/T calculations, then apply to circuit formulas as needed.
Sampling rate (Nyquist frequency) is critical for accurate digital signal representation:
- Nyquist rate: fsampling ≥ 2 × fmax (signal's highest frequency)
- Aliasing: If fsampling < 2fmax, higher frequencies appear as lower ones
- Audio CD: 44.1kHz sampling → captures up to 22.05kHz (beyond human hearing)
- Practical margin: Typically sample at 2.2-2.5 × fmax for safety
Example: To sample a 20kHz audio signal, use at least 40kHz sampling rate (CD uses 44.1kHz).
Several factors can cause discrepancies between calculated and measured frequencies:
- Component tolerances: Resistors/capacitors typically ±5-10%, crystals ±10-50ppm
- Parasitic effects: Stray capacitance/inductance at high frequencies
- Oscillator loading: Measuring circuit affects the oscillator frequency
- Timebase accuracy: Oscilloscope calibration error (usually ±0.01%)
- Temperature effects: Components change value with temperature
- Power supply variation: Frequency often depends on voltage
For critical applications, always measure with calibrated equipment and account for all parasitic elements.
Different units are appropriate for different frequency ranges:
- Hz (Hertz): Audio frequencies, power line (50/60Hz), human movement
- kHz (Kilohertz): Audio processing, ultrasound, AM radio, microcontroller clocks
- MHz (Megahertz): FM radio, computer buses, video signals, RF circuits
- GHz (Gigahertz): WiFi, Bluetooth, cellular, CPU clocks, satellite communications
- THz (Terahertz): Infrared, light, future wireless technologies
General rule: Use the unit that gives you numbers between 1 and 1,000. Example: 2,400,000 Hz = 2.4 MHz (easier to work with).